At what point does the normal to $y= 3 + 5x + 2x^2$ at $(1, 10 )$ intersect the parabola a second time?
( , )

The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. if the slope of the first line is $m$ then the slope of the second line is $- 1/m$